Related papers: Configuration Spaces of Surfaces

In this paper we study the spaces of $q$-tuples of points in a Euclidean space, without $k$-wise coincidences (configuration-like spaces). A transitive group action by permuting these points is considered, and some new upper bounds on the…

This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…

The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…

Configuration spaces of distinct labeled points on the plane are of practical relevance in designing safe control schemes for Automated Guided Vehicles (robots) in industrial settings. In this announcement, we consider the problem of the…

A natural kind of compactification of the virtual moduli spaces of rational functions of one complex variable is given. To describe the boundary points geometrically, the authors introduce the concept of rational functions with nodes,…

In this paper we calculate the homology of configuration spaces of $n$ points on a circle, subject to the condition that two pre-determined points are included in the configuration. We make use of discrete Morse theory both to determine the…

In this paper we first describe the geometry of the Newton polyhedra of polynomials invariant under certain linear Hamiltonian circle actions. From the geometry of the polyhedra, various Poisson structures on the orbit spaces of the actions…

We prove that the moduli spaces of K3 surfaces with non-symplectic involutions are unirational. As a by-product we describe configuration spaces of 4<d<9 points in the projective plane as arithmetic quotients of type IV.

We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be…

We consider orbit configuration spaces $C_n^G(S)$, where $S$ is a surface obtained out of a closed orientable surface $\bar{S}$ by removing a finite number of points (eventually none) and $G$ is a finite group acting freely continuously on…

The idea that possible configurations of a physical system can be represented as points in a multidimensional configuration space ${\cal C}$ is explored. The notion of spacetime, without ${\cal C}$, does not exist in this theory. Spacetime…

We prove orientation results for evaluation maps of moduli spaces of rational stable maps to del Pezzo surfaces over a field, both in characteristic $0$ and in positive characteristic. These results and the theory of degree developed in a…

Let G be a split semisimple algebraic group with trivial center. Let S be a compact oriented surface, with or without boundary. We define {\it positive} representations of the fundamental group of S to G(R), construct explicitly all…

This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…

We consider orbit configuration spaces associated to finite groups acting freely by orientation preserving homeomorphisms on the $2$-sphere minus a finite number of points. Such action is equivalent to a homography action of a finite…

We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a…

This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…

The differential-geometric structure of the manifold of smooth shapes is applied to the theory of shape optimization problems. In particular, a Riemannian shape gradient with respect to the first Sobolev metric and the Steklov-Poincar\'{e}…

Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…